Lecture 13: Validation
g
Motivation
gThe Holdout
g
Re-sampling techniques
gThree-way data splits
Motivation
g
Validation techniques are motivated by two fundamental
problems in pattern recognition: model selection and
performance estimation
g
Model selection
n Almost invariably, all pattern recognition techniques have one or more
free parameters
g The number of neighbors in a kNN classification rule
g The network size, learning parameters and weights in MLPs
n How do we select the “optimal” parameter(s) or model for a given
classification problem?
g
Performance estimation
n Once we have chosen a model, how do we estimate its performance?
g Performance is typically measured by the TRUE ERROR RATE, the
Motivation
g
If we had access to an unlimited number of examples these
questions have a straightforward answer
n Choose the model that provides the lowest error rate on the entire
population and, of course, that error rate is the true error rate
g
In real applications we only have access to a finite set of
examples, usually smaller than we wanted
n One approach is to use the entire training data to select our classifier
and estimate the error rate
g This naïve approach has two fundamental problems
n The final model will normally overfit the training data
g This problem is more pronounced with models that have a large number of
parameters
n The error rate estimate will be overly optimistic (lower than the true error rate) g In fact, it is not uncommon to have 100% correct classification on training
data
n A much better approach is to split the training data into disjoint subsets:
The holdout method
g Split dataset into two groups
n Training set: used to train the classifier
n Test set: used to estimate the error rate of the trained classifier
g A typical application the holdout method is determining a stopping
point for the back propagation error
Training Set Test Set
Total number of examples
Epochs MSE
Training set error Test set error Stopping point
The holdout method
g The holdout method has two basic drawbacks
n In problems where we have a sparse dataset we may not be able to afford the
“luxury” of setting aside a portion of the dataset for testing
n Since it is a single train-and-test experiment, the holdout estimate of error rate
will be misleading if we happen to get an “unfortunate” split
g The limitations of the holdout can be overcome with a family of
resampling methods at the expense of more computations
n Cross Validation
g Random Subsampling g K-Fold Cross-Validation
g Leave-one-out Cross-Validation
Random Subsampling
g
Random Subsampling performs K data splits of the dataset
n Each split randomly selects a (fixed) no. examples without replacement n For each data split we retrain the classifier from scratch with the training
examples and estimate Ei with the test examples
g
The true error estimate is obtained as the average of the
separate estimates E
in This estimate is significantly better than the holdout estimate Total number of examples
Experiment 1 Experiment 2 Experiment 3 Test example
∑
= = K 1 i i E K 1 EK-Fold Cross-validation
g
Create a K-fold partition of the the dataset
n For each of K experiments, use K-1 folds for training and the remaining
one for testing
g
K-Fold Cross validation is similar to Random Subsampling
n The advantage of K-Fold Cross validation is that all the examples in the
dataset are eventually used for both training and testing
g
As before, the true error is estimated as the average error rate
Total number of examples
Experiment 1 Experiment 2 Experiment 3 Test examples Experiment 4
∑
K 1Leave-one-out Cross Validation
g
Leave-one-out is the degenerate case of K-Fold Cross
Validation, where K is chosen as the total number of examples
n For a dataset with N examples, perform N experiments
n For each experiment use N-1 examples for training and the remaining
example for testing
g
As usual, the true error is estimated as the average error rate on
test examples
∑
= = N 1 i i E N 1 ETotal number of examples
Experiment 1 Experiment 2 Experiment 3
Experiment N
How many folds are needed?
gWith a large number of folds
+ The bias of the true error rate estimator will be small (the estimator will be very accurate)
- The variance of the true error rate estimator will be large
- The computational time will be very large as well (many experiments)
g
With a small number of folds
+ The number of experiments and, therefore, computation time are reduced
+ The variance of the estimator will be small
- The bias of the estimator will be large (conservative or higher than the true error rate)
g
In practice, the choice of the number of folds depends on the
size of the dataset
n For large datasets, even 3-Fold Cross Validation will be quite accurate n For very sparse datasets, we may have to use leave-one-out in order to
train on as many examples as possible
Three-way data splits
g
If model selection and true error estimates are to be computed
simultaneously, the data needs to be divided into three disjoint
sets
n Training set: a set of examples used for learning: to fit the parameters
of the classifier
g In the MLP case, we would use the training set to find the “optimal” weights
with the back-prop rule
n Validation set: a set of examples used to tune the parameters of of a
classifier
g In the MLP case, we would use the validation set to find the “optimal”
number of hidden units or determine a stopping point for the back propagation algorithm
n Test set: a set of examples used only to assess the performance of a
fully-trained classifier
g In the MLP case, we would use the test to estimate the error rate after we
have chosen the final model (MLP size and actual weights)
g After assessing the final model with the test set, YOU MUST NOT further
Three-way data splits
g
Why separate test and validation sets?
n The error rate estimate of the final model on validation data will be
biased (smaller than the true error rate) since the validation set is used to select the final model
n After assessing the final model with the test set, YOU MUST NOT tune
the model any further
g
Procedure outline
n This outline assumes a holdout method
g If CV or Bootstrap are used, steps 3 and 4 have to be repeated for each of 1. Divide the available data into training, validation and test set
2. Select architecture and training parameters 3. Train the model using the training set
4. Evaluate the model using the validation set
5. Repeat steps 2 through 4 using different architectures and training parameters 6. Select the best model and train it using data from the training and validation set 7. Assess this final model using the test set
1. Divide the available data into training, validation and test set 2. Select architecture and training parameters
3. Train the model using the training set
4. Evaluate the model using the validation set
5. Repeat steps 2 through 4 using different architectures and training parameters 6. Select the best model and train it using data from the training and validation set 7. Assess this final model using the test set
